OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..449
FORMULA
a(n) = (-1)^(n+1)*floor(n!*sinh(1)), n>=1. - Vladeta Jovovic, Aug 10 2002
Let u(1) = 1, u(n) = n*u(n-1) + n (mod 2); then for n>0, a(n) = (-1)^(n+1)*u(n). - Benoit Cloitre, Jan 12 2003
Unsigned sequence satisfies a(n) = n*a(n-1)+a(n-2)-(n-2)*a(n-3), with E.g.f. sinh(z)/(1-z). - Mario Catalani (mario.catalani(AT)unito.it), Feb 08 2003
a(n) = (-1)^(n+1) * n! * Sum_{k=1..floor((n+1)/2)} 1/(2*k-1)!.
a(n) = -n*a(n-1) + n (mod 2). - Seiichi Manyama, Sep 09 2016
a(n) = (-1)^n*(exp(-1)*Gamma(1+n,-1) - exp(1)*Gamma(1+n,1))/2. - Peter Luschny, Dec 18 2017
MAPLE
G(x):= sinh(x)/(1+x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..20); # Zerinvary Lajos, Apr 03 2009
MATHEMATICA
a[n_] := (-1)^n (Exp[-1] Gamma[1 + n, -1] - Exp[1] Gamma[1 + n, 1])/2;
Table[a[n], {n, 0, 20}] (* Peter Luschny, Dec 18 2017 *)
With[{nn=30}, CoefficientList[Series[Sinh[x]/(1+x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 19 2023 *)
PROG
(PARI) a(n) = n!*polcoeff((sinh(x)/(1+x) + x * O(x^n)), n) \\ Charles R Greathouse IV, Sep 09 2016
(PARI) x='x+O('x^99); concat([0], Vec(serlaplace(sinh(x)/(1+x)))) \\ Altug Alkan, Dec 18 2017
(Ruby)
def A009628(n)
a = 0
(0..n).map{|i| a = -i * a + i % 2}
end # Seiichi Manyama, Sep 09 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified by Harvey P. Dale, Mar 19 2023
STATUS
approved